Pion-Nucleon Coupling Constant and Scattering Phase Shifts

Goldberger's relations for the forward scattering of pions are used in the following way. Two linear functions of ${\nu }^2$, where $\nu$ is the total pion energy in the laboratory system, are constructed from quantities taken from experiment, i.e., forward amplitudes and integrals over total cross sections. The extrapolation of one of these functions to $\nu =0\mathrm{}$ gives $2f^2$, where $f$ is the renormalized pion-nucleon coupling constant. Various sets of phase shifts are compared as to their compatibility with the above functions.